Korn-Poincaré inequalities for functions with a small jump set
Korn-Poincaré inequalities for functions with a small jump set
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小跳跃集函数的 Korn-Poincaré 不等式
DOI：
10.1512/iumj.2016.65.5852
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发表时间：
2016
影响因子：
1.1
通讯作者：
G. Francfort
中科院分区：
文献类型：
--
作者：
A. Chambolle;S. Conti;G. Francfort
在几何线性断裂模型的研究中，自然会出现“变形有界的特殊函数”和p-可积应变。它们有一个有限（n − 1）维测度的跳集，并且在远离跳集的地方，有一个Lp中的对称梯度e（u），p ≥ 1。我们表明，如果测量的跳跃集是足够小的域的大小，那么函数u可以近似仿射函数远离一个小的例外集，与误差仅取决于e（u）。我们还导出了相应的跟踪语句。
"Special functions with bounded deformation" and p-integrable strain arise naturally in the study of geometrically linear fracture models. They have a jump set of finite (n − 1)-dimensional measure and, away from the jump set, a symmetrized gradient e(u) in Lp , p ≥ 1. We show that if the measure of the jump set is sufficiently small with respect to the size of the domain, then the function u can be approximated by an affine function away from a small exceptional set, with an error which depends solely on e(u). We also derive a corresponding trace statement.